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Fractal dimensions of percolating networks

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  • Cohen, Reuven
  • Havlin, Shlomo

Abstract

We use the generating function formalism to calculate the fractal dimensions for the percolating cluster at criticality in Erdős–Rényi (ER) and random scale free (SF) networks, with degree distribution P(k)=ck−λ. We show that the chemical dimension is dl=2 for ER and SF networks with λ>4, as in percolation in d⩾dc=6 dimensions. For 3<λ<4 we show that dl=(λ−2)/(λ−3). The fractal dimension is df=4 (λ>4) and df=2(λ−2)/(λ−3) (3<λ<4), and the embedding dimension is dc=6 (λ>4) and dc=2(λ−1)/(λ−3) (3<λ<4). We discuss the meaning of these dimensions for networks.

Suggested Citation

  • Cohen, Reuven & Havlin, Shlomo, 2004. "Fractal dimensions of percolating networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 6-13.
    • Handle: RePEc:eee:phsmap:v:336:y:2004:i:1:p:6-13
    DOI: 10.1016/j.physa.2004.01.005
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    Cited by:

    1. Kolumbus, Yoav & Solomon, Sorin, 2021. "On the influence maximization problem and the percolation phase transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).

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